To solve the equation under the given parameters, we know that the cosine function equals to -1/2. Our task is to find the values for x that satisfy this condition on the interval from 0 to 360 degrees.
From our knowledge of trigonometry, we recall the property that cosine is positive in quadrants I and IV, and negative in quadrants II and III in the trigonometric circle. This is commonly referred to as the "ASTC" or "All Students Take Calculus" rule, indicating whether the sine (S), cosine (C), or tangent (T) is positive in each quadrant (A is for all, meaning all three are positive in quadrant I).
Given that cos(x) equals to -1/2, we can clearly infer that x will lie in Quadrant II or Quadrant III. This is because cosine is negative in these quadrants, implying cos(x) is negative as well.
Now, we need to find the reference angle (θ), such that cos(θ) equals to 1/2. This reference angle can be calculated using the inverse cosine function: θ = cos^-1(1/2), which gives approximately θ = 60 degrees. Remember that we're dealing with a negative cosine value, so our actual angles will be the ones in Quadrant II and III that have the same cosine value as 60 degrees in Quadrant I.
Our corresponding angle in the second quadrant will be simply θ = 180 - 60 = 120 degrees. This is because, in second quadrant, angles range from 90 to 180 degrees.
Our corresponding angle in the third quadrant will be θ = 180 + 60 = 240 degrees. In third quadrant, angles range from 180 to 270 degrees.
However, it seems that there might have been a mistake in the answer provided. Conventionally, for a cosine value of -1/2, our angles should lie at 120 and 240 degrees in the second and third quadrant respectively. However, as per the given answer, the angle in the third quadrant is stated as 300 degrees.
Please double check the provided solution or confirm whether there's a special condition or assumption involved that leads to this value of 300 degrees. Based on standard trigonometric principles, the expected angles for cos(x) = -1/2 should be 120 and 240 degrees.